and on Astronomical Refi'actions. 439 



Laplace arrived at this equation (Mec. Cel. vol. v. p. 128.). 



See Poisson, Aimales deChimie et de Physique, torn, xxiii. p. 342*^; 



Mecanique, vol. ii. p. 648 ; Navier, Lecons donnees a I'Ecole des Fonts 



et Chaiissees, torn. ii. 



l_ 1 



V^A + bP-'' V' = A + BPr' 



p = kg{l +ccQ) p' = kg'{l + uQ') 



k and a. being constants. 



I will now introduce the additional condition that the heat is _pro- 

 portional to the temperature, in which case 



F = C' + Z)(i +aa) 



C and D being constants. These equations include implicitly the 

 hypothesis attributed to Watt and also that of Southern, respect- 

 ing the vapour of water : on the former Z) = 0. Hence 



j_ 



V = C + D (1 + u&) = A + B ^'^ 



F'= C+ Z)(l + a6') =A-\- B^'^ 



P 



P 



1 + «6' = (1 + «fl) 



kB 

 D 



If j—^ = E and if 6 correspond to the boiling point, Q — 180<^ 



in Fahrenheit's scale, if the pressure be measured in atmospheres 

 p = 1, but generally 



[* A translation of M. Poisson's memoir here referred to vUl be found in Phil. 

 First Series, vol. Ixii. p. 328. — Edit.] 



-f- This equation must not be confounded with another equation which may be deduced 

 from it by making E = 0, and which is not reconcileable with phenomena, as was 

 long since noticed by M. Poisson in the case of steam. An equation of this kind is given 

 by M. Pouillet in the form 



